Mathematics, 26.07.2019 12:00 TVASALLO31

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A) To find the percent of Hal's backyard taken up by the patio, walkway, and garden, you need to find the total area taken up by those three places, divide that number by the total area of his backyard, and multiply that number by 100% to get the percentage taken up by those three places.

Start by finding the area of each of the three places, then add them together to find the total area taken up by the three places. Hal's backyard is created from many rectangular parts. Remember that the equation for the area of a rectangle is: A = lw

, where A = area, l = length, w = width

1) The length of the patio, l = 9 ft (since it's as long as the lawn beneath it). The width, w = 6ft. Plug that into the equation for area of a rectangle to find area of the patio:
$A = lw\\
A = (9)(6)\\
A = 54 ft^{2}$

2) The length of the walkway, l = 2 ft (since the length of the garden plus lawn is 9ft, minus the 7ft of the garden because the garden is as long as the 7ft lawn above it). The width of the walkway, w = 10ft (width of patio plus garden). Plug that into the equation for the area of a rectangle to find area of the walkway:
$A = lw\\
A = (2)(10)\\
A = 20 ft^{2}$

3) The length of the garden, l = 7ft (since the garden is as long as the 7ft lawn above it). The width of the garden is 4ft. Plug that into the equation for the area of a rectangle to find area of the garden:
$A = lw\\
A = (7)(4)\\
A = 28ft^{2}$

4) Add up the areas of the patio, walkway, and garden to find total area of the three places:
$54ft^{2} + 20ft^{2} + 28 ft^{2} = 102 ft^{2}$

Now find the total area of the entire backyard using the equation for the area of the rectangle. We know that length of the backyard l = 18ft, and the width of the backyard w = 10ft. Plug those numbers into the equation:
$A = lw\\
A = (18)(10\\
A = 180 ft^{2}$

Finally, divide the total area of the three places by the total area of the backyard and multiply that decimal by 100% to get the percentage:
$\frac{102}{180} \times 100 \% = 56.666\%$ ≈ 57%

The percent of the whole backyard taken up by the three places is 57%.

B) To solve this question, you need to find the length of the three sides of the yard not touching his house and multiply that length by $10.75 because that is how much the fence costs per foot.

The longer side lies along his house, so we don't include one of the 18ft sides. The other three sides are 10ft and 10ft (the length of the shorter two sides) and 18ft (the long side across from his house). Add those three lengths together to get the length of the fencing needed: 10ft + 10ft + 18ft = 38ft.

Since fencing is $10.75/ft, multiply 38ft by $10.75: 38ft*$10.75 = $408.50.

Your answer is $408.50.

Answer from: Quest

The answer for this question is 80
Special angles type 2 measure of angle 1 40 80 160

Answer from: Quest

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